I remember chanting this with hundreds of other demonstrators as we marched against the war in Vietnam. We knew the war was a vicious travesty and that the president’s lies had forced us into it. When a weary-looking Lyndon Baines Johnson announced on television in 1968, “I shall not seek, and I will not accept, the nomination of my party for another term as your president,” we rejoiced as only self-righteous young true believers can: We had won. We had toppled the monster.

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Over the past several years, thanks to the work of such historians as Robert Caro, a far more morally complex picture of Johnson has emerged. In particular, we have come to understand his role in passing the Civil Rights Act of 1964 after the assassination of President John F. Kennedy, and have some idea of his reasons for undertaking the War on Poverty. Some experts believe that if it weren’t for the entanglement of Vietnam, Johnson would be remembered as a great president, a worthy successor to FDR. Whatever he accomplished, as Robert Schenkkan reveals in his engrossing All the Way (the title is based on the slogan “All the Way With LBJ”), Johnson managed it in his own inimitable way. Having come up from a hardscrabble background — one the high-born Kennedys mocked mercilessly — he had viewed power from the bottom up and understood deeply and intuitively how it works. As with so many larger-than-life historical figures, the forces of good and evil were inextricably mingled in Johnson.

Schenkkan’s play, a 2014 Tony winner, illustrates Johnson’s tactics, both brilliant and crude, a combination of bullying, wheedling, threats and promises. LBJ had to make compromises, but he knew that if he bided his time, he’d eventually get what he wanted. Martin Luther King Jr., his ally and adversary, had to compromise, too, with militant activists like Stokely Carmichael breathing fire on one side, a president who promised great gains in exchange for difficult sacrifices on the other, and FBI head J. Edgar Hoover monitoring his conversations and — unbeknownst to him — taping his sexual infidelities.

The Denver Center has fielded an unusually large cast, with several actors playing more than one role, sometimes confusingly — and all of the other characters are far less fleshed out than LBJ. I understand that Brian Cranston of Breaking Bad fame gave a forceful portrayal of LBJ on Broadway; C. David Johnson’s interpretation is more subdued. He does full justice to all the crude folksiness — “Not too tight in the bunghole, and leave me some slack for my nut sack,” LBJ says to a tailor fitting him for a suit — but you can see ideas contending silently in his mind. And by the second act, when the president, at first so confidently energetic, is feeling demoralized and self-pitying, the most thin-skinned of bullies, the actor communicates all the complexities of this flawed great man.

The script does give some of Johnson’s relationships contour and warmth. It’s a pleasure to watch him sparring with his longtime mentor, Senator Richard Russell (a wonderful portrayal by Philip Pleasants, by turns warm, threatening and resigned). We also see his fatherly feelings toward Walter Jenkins (Jeffrey Roark, gently self-effacing), whom he eventually betrays. And there are a couple of telling scenes with Lady Bird (sympathetically played by Kathleen McCall). Terence Archie walks in Martin Luther King’s shoes with dignity.

This is a talky play. It’s three hours long, and much of the talk is about politics and procedure, bills being bottled up, maneuverings to get them unbottled, ways of beating or playing the system. Yet I never lost interest for a second. Schenkkan has created a fascinating diorama that still manages to breathe, and at the same time, he keeps the action moving forward. He sheds light on some current political realities, too, including the degradation of the Republican Party as the Democrats become the party of racial justice and Dixiecrats defect. “The Democratic Party just lost the South for the rest of my lifetime and maybe yours,” LBJ observes. And Schenkkan clarifies the issue of whether Johnson’s actions on civil rights stemmed more from conviction or political expediency with a well-chosen, real-life LBJ quote: “What’s the point of being a president if you can’t do what you know is right?”

All the Way , presented by the Denver Center for the Performing Arts through February 28, Stage Theatre, Denver Performing Arts Complex, 303-893-4100, denvercenter.org.